Prescribed-Time Stabilization of Nonlinear Systems with Uncertain Input Gain and Non-Vanishing Disturbances

A partial-state-feedback prescribed-time stabilizing controller is designed for a class of nonlinear systems with uncertain input gain, nonlinear uncertainties throughout the system dynamics involving both parametric and functional uncertainties, and time-varying non-vanishing disturbances generated by an appended dynamics. A dynamic adaptive controller is designed using a temporally transformed system representation in combination with a dynamic high-gain scaling based design procedure, and guarantees convergence of system state to the origin in the finite prescribed time.